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Author Topic: Help: Mandelbrot pertubation fails when zooming deeper than 1E1400  (Read 1132 times)
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CFJH
Alien
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Posts: 31


« on: January 04, 2014, 11:20:00 PM »

Hello,
over the last days I experimented with my own fractal programm.
Currently I'm using only formula (1) from the sft document.
All calculations are done with long double 80 bit datatype, except the calculation of the reference point, where the GMP ist used.
Using the pertubation method now I found an error which I can't solve so far.

My current strategy is that I render small preview images with classic method to find/serch the destination. From the final image (with the minibrot) I compute the reference point and store the coefficients to a file.

The coordinates of the last image (attachment zp49_02989.jpg) :
Code:
mag=2.88024294864E2898
re=-0.228155493653961819214572014099126006737398351174508032379597981084415663036013066757421042711970437268939585386816469905360621768338929494238545390547353638503609151421208524788914955240718294649807399935999858816761369110006545501557947692511511536454828040448704636885667280398091611692374593524757189049141208420826812720100422874424982340170961075331068635883166081123269331016270098508361087077833154904324128264646204875932111444055804466980483012672723385931778337635951396292680216269878880929835721290940928138383036870128422877754678479378687051458498619808443944509984422719612504135983526148008466137865522665206222773200779260364022367950008156274210921001880108008314196073519829157791111634729470143710974893284477142277011069100090989918573842548583093041902409948263341207430845320627499806440266007807543988047999738958151286666046206551168115350844720738507133334406506452653595940075715923094608687884106538641949638234295555296508465577821151329306573686581379031862139316537865731512838172855479903298991578351489606840726611917981648696455854495480128253062002382824250864806171913970931008751474727225679181892630170444822162895840361277130105613864721353386423980667073024401175253401896396788209829755777820245161381601753515409160039758973533401181997278485827483182910166596719767738728693166928637632784068782877190200295915254857274809471379496091646052013653639158342906746821293477913861568838883162508227904940592508445082832451094658206070098108058371499803649262117527097081413044083361371066562956251606064550396670436453133336843005979891413645252634762472806536140083325083138834362873191797281507404788371661076451637908700257130578425313739088067922629601851900202306008656761349160170558054821783077427764971183638001976349030976540281059522366013490521318344494287825685683972005527548036903310243006117066821357863163417718657147681576891356822300948581194675279315162224403341879221739693797168925504499853355954355097038417524184580534783324042600624855594990648364249951166541789910527250646087684769157019315871077158701215895802129773414646582733370820644962213082363328203580749681294300016115452252455780732890426284986018411506856737674248839731009232410619262857692323992181178234570681591072148145279796792612534059038350091094969036678923079241620953258130319909153216181918642707776439297254842289395124971560595103914480136002250360380366789164501164021379143331637487422735109296178368448899890272880744288366530693237328421749021060696378904658674381112889857888727687242477971774241610970182520730551962045872256188999246396137554806824561283588046355838032402489833186295579971346325691464314115816938957352245127984517726729703131805459280137083921764482057913128936333458972465378578968319882929449933370450102446539616181407642051022841037512367677547833701068597069387195752871063339289690965027892986185709373603425376298321308954932257916427885866623571044189454
im=1.1151425080399373597457646363150140681887780904679546036274680334810409092946355168572572006874765228872100322451033324674089490817457188452599842530139888003789611498451538187135582267447926710194039382369014758821696953203973909890684815787539535821296738902997986221240372961651516963059575999816402095033448363132460536005643111932958088293412160670689807879737489438573051324049431610845845747954843962673151100894218512451430034482302328794196056334954411558991905342112112527527903101934319426939125067685400406793219409258237634837567486913882656202820651153459408007214812446063004016990478652901305445641122501686263488595219535793985626639534336539014265204709419139006829819188034750141155411193942246951711574277826630794139256362861546610055511351508465695050691949963483822796221939931284629304822712266585418510537313581792664669885462998369057457995067178653752112010687171006981485870807732922069316869110790300072072961715073179740733857227860008589343847074244422121264906898067851895317160951594245327166628108445186252755952562820517988653414929514419637982778276100132099044433881697905459607257608704571044608840074600309371170216417153702491354786271482917736397381910879181445890339571901612161824780067385824034904436695525460581789870754064314359375849781174311237014600685868261161702827885199481741564438007098545323618020438796286585378653666144021361273489608750774381256160101950998522642093298816512318824240203295362977204772074460983061335733453289220960361273409315843918512887588053023715941861535225775429375759015715633393748709688013165752203810756242094878573353612094730613240777870652441806811252784643578997978414892546008070868023070747066206136774534412629745372683863679282378169357137066484245197250072336080141492007754525005486530094823130207333560286412822695456193472387286376424371240431060509001478621687281443210037065314193343618601793870015025387509766440356455882647611930693616127361505861471995759634443772740541616692106177742144352735744095844199462629413973080316955741894123134334902602570947329407545843053855340696592190717100838849013734180856505792043366349580277646631461376896978255186945840215922875749111283561204003335890235067985143510968326747002049195838337080988192303737065403326741832397443406356733892505198041781305606875612762932951292773275293846272679425063624136210734658811593428349846101949855305243090175870138182920684489434323316137210867670470427033067914111333436480844643340923940374500495312223151203285993936839272213248991819604992074915090477549511648617468307425977988429768060170998567455827405676228064241314809243394200295517516898896908251562377157190452790952630454750281401919398985141306754952210761711380933635198919292677892763674067677938401345844814645204200417440700040927453875886834756769956564930870727588540356647641850358821048775347902381456140582213325789250363676047238936614189747321052837198997491256584375

The coefficients file looks like this:

Code:
1  -1.419643377607080481084267376e+00   6.062907292071992859661122566e-01
2   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
3   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
4   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
...

Then I reuse this values for computing all frame for the animation.

My problem ist now, when I reach (approx) zoom level 1.0E+1400, the classic rendered and pertubation renderes images get different.
Some details are going lost ans it seems that the pertubation redered images are auto-centered to a minibrot ?!?

Image parameters, where I get first differences:
Code:
Mag=1.0E1350
re=-0.228155493653961819214572014099126006737398351174508032379597981084415663036013066757421042711970437268939585386816469905360621768338929494238545390547353638503609151421208524788914955240718294649807399935999858816761369110006545501557947692511511536454828040448704636885667280398091611692374593524757189049141208420826812720100422874424982340170961075331068635883166081123269331016270098508361087077833154904324128264646204875932111444055804466980483012672723385931778337635951396292680216269878880929835721290940928138383036870128422877754678479378687051458498619808443944509984422719612504135983526148008466137865522665206222773200779260364022367950008156274210921001880108008314196073519829157791111634729470143710974893284477142277011069100090989918573842548583093041902409948263341207430845320627499806440266007807543988047999738958151286666046206551168115350844720738507133334406506452653595940075715923094608687884106538641949638234295555296508465577821151329306573686581379031862139316537865731512838172855479903298991578351489606840726611917981648696455854495480128253062002382824250864806171913970931008751474727225679181892630170444822162895840361277130105613864721353386423980667073024401175253401896396788209829755777820245161381601753515409160039758973533401181997278485827483182910166596719767738728693166928637632784068782877190200295915254857274809471379496091646052013653639158342906746821293477913861568838883162508227904940592508445082832451094658206070098108058371499803649262117527097081413044083361371066562956251606064550396670436453133336843005979891413645252634762472806536140083325083138834362873191797281507404788371661076451637908700257130578425313739088067922629601851900202306008656761349160170558054821783077427764971183638001976349030976540281059522366013490521318344494287825685683972005527548036903310243006117066821357863163417718657147681576891356822300948581194675279315162224403341879221739693797168925504499853355954355097038417524184580534783324042600624855594990648364249951166541789910527250646087684769157019315871077158701215895802129773414646582733370820644962213082363328203580749681294300016115452252455780732890426284986018411506856737674248839731009232410619262857692323992181178234570681591072148145279796792612534059038350091094969036678923079241620953258130319909153216181918642707776439297254842289395124971560595103914480136002250360380366789164501164021379143331637487422735109296178368448899890272880744288366530693237328421749021060696378904658674381112889857888727687242477971774241610970182520730551962045872256188999246396137554806824561283588046355838032402489833186295579971346325691464314115816938957352245127984517726729703131805459280137083921764482057913128936333458972465378578968319882929449933370450102446539616181407642051022841037512367677547833701068597069387195752871063339289690965027892986185709373603425376298321308954932257916427885866623571044189454
im=1.1151425080399373597457646363150140681887780904679546036274680334810409092946355168572572006874765228872100322451033324674089490817457188452599842530139888003789611498451538187135582267447926710194039382369014758821696953203973909890684815787539535821296738902997986221240372961651516963059575999816402095033448363132460536005643111932958088293412160670689807879737489438573051324049431610845845747954843962673151100894218512451430034482302328794196056334954411558991905342112112527527903101934319426939125067685400406793219409258237634837567486913882656202820651153459408007214812446063004016990478652901305445641122501686263488595219535793985626639534336539014265204709419139006829819188034750141155411193942246951711574277826630794139256362861546610055511351508465695050691949963483822796221939931284629304822712266585418510537313581792664669885462998369057457995067178653752112010687171006981485870807732922069316869110790300072072961715073179740733857227860008589343847074244422121264906898067851895317160951594245327166628108445186252755952562820517988653414929514419637982778276100132099044433881697905459607257608704571044608840074600309371170216417153702491354786271482917736397381910879181445890339571901612161824780067385824034904436695525460581789870754064314359375849781174311237014600685868261161702827885199481741564438007098545323618020438796286585378653666144021361273489608750774381256160101950998522642093298816512318824240203295362977204772074460983061335733453289220960361273409315843918512887588053023715941861535225775429375759015715633393748709688013165752203810756242094878573353612094730613240777870652441806811252784643578997978414892546008070868023070747066206136774534412629745372683863679282378169357137066484245197250072336080141492007754525005486530094823130207333560286412822695456193472387286376424371240431060509001478621687281443210037065314193343618601793870015025387509766440356455882647611930693616127361505861471995759634443772740541616692106177742144352735744095844199462629413973080316955741894123134334902602570947329407545843053855340696592190717100838849013734180856505792043366349580277646631461376896978255186945840215922875749111283561204003335890235067985143510968326747002049195838337080988192303737065403326741832397443406356733892505198041781305606875612762932951292773275293846272679425063624136210734658811593428349846101949855305243090175870138182920684489434323316137210867670470427033067914111333436480844643340923940374500495312223151203285993936839272213248991819604992074915090477549511648617468307425977988429768060170998567455827405676228064241314809243394200295517516898896908251562377157190452790952630454750281401919398985141306754952210761711380933635198919292677892763674067677938401345844814645204200417440700040927453875886834756769956564930870727588540356647641850358821048775347902381456140582213325789250363676047238936614189747321052837198997491256584375
Image classig rendered: zp49_1350.jpg
Image pertubation rendered: zp49_1350a.jpg

In the pertubation rendered image are two differences:
- the center is different, and all following images are different too.
- the zoom should pass the spiral, but the pertubation rendered images are centered.

I've done a second zoom with nearly the different result.
Also I wrote my program new from scratch also with the same result (if needed, I can post the code or parts of it).

I've no Idea what is going wrong
 - reusing one reference point for all images
 - is long double precise enough
 - hardware defect
??

Had anyone else similar problems and give me a hint ?

Jürgen


* zp49z_02989.jpg (22.36 KB, 256x192 - viewed 325 times.)

* zp49z_01350.jpg (24.52 KB, 256x192 - viewed 323 times.)

* zp49z_01350a.jpg (24.35 KB, 256x192 - viewed 328 times.)
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element90
Strange Attractor
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Posts: 298



WWW
« Reply #1 on: January 04, 2014, 11:41:02 PM »

This may not help at all.

You don't say which platform you are programming for, if it is Windows using Microsoft's compiler then long double is just a synonym for double and consequently is 64 bits.
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Elelemt90 Fractals blog www.element90.wordpress.com
CFJH
Alien
***
Posts: 31


« Reply #2 on: January 05, 2014, 12:08:58 AM »

I'am running suse Linux 13.1 and compile with gcc

Code:
gcc --version
gcc (SUSE Linux) 4.8.1 20130909 [gcc-4_8-branch revision 202388]
Copyright (C) 2013 Free Software Foundation, Inc.

Jürgen
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Pauldelbrot
Fractal Senior
******
Posts: 2592



pderbyshire2
« Reply #3 on: January 05, 2014, 01:18:21 AM »

Do you have intermediate results that, at zoom 1E1400, get close to 1E5000? Because if so you could be running up against the maximum exponent of an 80-bit long double.
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Kalles Fraktaler
Fractal Senior
******
Posts: 1458



kallesfraktaler
WWW
« Reply #4 on: January 05, 2014, 10:23:21 AM »

Hi CFJH

I don't have similar problems, regardless if series approximation is applied or not.
Attached image was rendered in Kalles Fraktaler.


* CFJH.jpg (116.38 KB, 640x360 - viewed 86 times.)
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claude
Fractal Bachius
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Posts: 563



WWW
« Reply #5 on: January 05, 2014, 01:01:12 PM »

The coefficients file looks like this:

Code:
1  -1.419643377607080481084267376e+00   6.062907292071992859661122566e-01
2   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
3   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
4   1.419643377607080481084267376e+00  -6.062907292071992859661122566e-01
...

...

I've no Idea what is going wrong
 - reusing one reference point for all images
 - is long double precise enough
 - hardware defect
??

Had anyone else similar problems and give me a hint ?

Jürgen

I think the coefficients file might be off by one iteration - if you start from z=0 then the first reference coordinate should be the c value for the reference.

Also using one reference point for all frames causes issues near other minibrots you pass along the way, and there is one near the depth you mentioned:

Code:
  period   = 1901
  real     = -0.22815549365396181921457201409912600673739835117450803237959798108441566303601306675742104271197043726893958538681646990536062176833892949423854539054735363850360915142120852478891495524071829464980739993599985881676136911000654550155794769251151153645482804044870463688566728039809161169237459352475718904914120842082681272010042287442498234017096107533106863588316608112326933101627009850836108707783315490432412826464620487593211144405580446698048301267272338593177833763595139629268021626987888092983572129094092813838303687012842287775467847937868705145849861980844394450998442271961250413598352614800846613786552266520622277320077926036402236795000815627421092100188010800831419607351982915779111163472947014371097489328447714227701106910009098991857384254858309304190240994826334120743084532062749980644026600780754398804799973895815128666604620655116811535084472073850713333440650645265359594007571592309460868788410653864194963823429555529650846557782115132930657368658137903186213931653786573151283817285547990329899157835148960684072661191798164869645585449548012825306200238282425086480617191397093100875147472722567918189263017044482216289584036127713010561386472135338642398066707302440117525340189639678820982975577782024516138160175351540916003975897353340118199727848582748318291016659671976773872869316692863763278406878287719020029609235218835034479454176514705404807585782628139149468021449802352446
  imag     = 1.11514250803993735974576463631501406818877809046795460362746803348104090929463551685725720068747652288721003224510333246740894908174571884525998425301398880037896114984515381871355822674479267101940393823690147588216969532039739098906848157875395358212967389029979862212403729616515169630595759998164020950334483631324605360056431119329580882934121606706898078797374894385730513240494316108458457479548439626731511008942185124514300344823023287941960563349544115589919053421121125275279031019343194269391250676854004067932194092582376348375674869138826562028206511534594080072148124460630040169904786529013054456411225016862634885952195357939856266395343365390142652047094191390068298191880347501411554111939422469517115742778266307941392563628615466100555113515084656950506919499634838227962219399312846293048227122665854185105373135817926646698854629983690574579950671786537521120106871710069814858708077329220693168691107903000720729617150731797407338572278600085893438470742444221212649068980678518953171609515942453271666281084451862527559525628205179886534149295144196379827782761001320990444338816979054596072576087045710446088400746003093711702164171537024913547862714829177363973819108791814458903395719016121618247800673858240349044366955254605817898707540643143593758497811743112370146006858682611617028278851994817415644380070985453236180201493847340663356878839980345306436896898049487597632853026068415535
  size     = 3.4676963688e-1408

I wouldn't be surprised if you also have problems around 1e-1002 and 1e-504 near passing other minibrots.  Embedded julia sets can also cause glitches with the perturbation technique when an unsuitable reference point is used.

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CFJH
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« Reply #6 on: January 08, 2014, 12:00:16 AM »

I think the coefficients file might be off by one iteration - if you start from z=0 then the first reference coordinate should be the c value for the reference.
This was my mistace, I posted a wrong file. Normally the iterations will begin with line 0 wich is the center of the image. Trying to find the error, one test was to remove the first line.
Quote

Also using one reference point for all frames causes issues near other minibrots you pass along the way, and there is one near the depth you mentioned:
I wouldn't be surprised if you also have problems around 1e-1002 and 1e-504 near passing other minibrots.  Embedded julia sets can also cause glitches with the perturbation technique when an unsuitable reference point is used.
In the meantime I've tested with a litte deeper zommed image. Using the reference marked with the red dot left on the left image (this is calculated with classic method), the pertubation rendered image is the second image :-( How can I find a good reference point ? When rendering an unknown image, I think the first reference is in the center. But when non trivial parts (or the hole image) is wrong, how can I correct it ?

Do you have intermediate results that, at zoom 1E1400, get close to 1E5000? Because if so you could be running up against the maximum exponent of an 80-bit long double.
Don't know. When lacking precistion will the image get blocks like an defect jpg or will I simply get wrong images. If yes, I will try to implement a new version using the GMP  with small fixed numbers (192 bit or so) ?


* zp49z_01351.jpg (23.88 KB, 256x192 - viewed 300 times.)

* zp49z_01351b.jpg (22.18 KB, 256x192 - viewed 295 times.)
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Kalles Fraktaler
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« Reply #7 on: January 08, 2014, 12:40:24 PM »

In the meantime I've tested with a litte deeper zommed image. Using the reference marked with the red dot left on the left image (this is calculated with classic method), the pertubation rendered image is the second image :-( How can I find a good reference point ? When rendering an unknown image, I think the first reference is in the center. But when non trivial parts (or the hole image) is wrong, how can I correct it ?
We haven't found an answer to your question yet.
I have found some ways to solve glitches, but they are not perfect.
See this post on my thread http://www.fractalforums.com/index.php?topic=16402.msg69818#msg69818 - use it as a base for further investigations and development and please share anything you find smiley
You can find many other posts in my thread and in http://www.fractalforums.com/index.php?topic=15559.0 about this glitch-solving/reference-picking topic, but so far there is no waterproof method found yet.
Don't know. When lacking precistion will the image get blocks like an defect jpg or will I simply get wrong images. If yes, I will try to implement a new version using the GMP  with small fixed numbers (192 bit or so) ?
Usually glitches are one-colored (one-iteration-count) blobs, as I showed on my images on the post above.
However a second type of glitch may occur, that contains pattern and is very hard to detect from a program.
http://www.fractalforums.com/index.php?topic=15559.msg67709#msg67709

But I think you are doing something else wrong, and that it should be possible to render that image decently with double or long double only. At which depth is that image?
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Pauldelbrot
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« Reply #8 on: January 08, 2014, 01:11:56 PM »

However a second type of glitch may occur, that contains pattern and is very hard to detect from a program.
http://www.fractalforums.com/index.php?topic=15559.msg67709#msg67709

I guess you deleted those images and then forgot about it, because the post you referenced has no images anymore and the links to them give 404 errors. You might want to put those files back on your server so the OP of this thread can see them when reading your message later.
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Kalles Fraktaler
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« Reply #9 on: January 08, 2014, 05:06:12 PM »

I guess you deleted those images and then forgot about it, because the post you referenced has no images anymore and the links to them give 404 errors. You might want to put those files back on your server so the OP of this thread can see them when reading your message later.
But they are there when I am looking at them now...? Please try again.
There has been problems with the swedish site biphome.spray.se and others due to a problem at a large provider last week but it should be solved by now...
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Kalles Fraktaler
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« Reply #10 on: January 08, 2014, 06:55:10 PM »

It seems that the images are cached in my browser and that the site is down.
I read that they are trying to recover the site, but they have been doing so since late November so I don't know if they will ever make it stable again.
But it did work in the beginning of January when I put the latest version of my program.

Anyway, the location of the glitch I mentioned is
Code:
Re: -1.9855484133529534182456788035170260405619874319858542762764067468457111296182870871016850697411093334121619737798
Im: 0.0000000000002743067126729694556175287646032154237263455024187599021148858835848003264687216859030875018929505969
Zoom: 7.06400000000E72
Iterations: 143411

Since the zoom pass a "tentacle" of a minibrot, shown in the first image, the effect is a "rain-deer horn" of higher iterations repeating with increasing frequency, and it causes a glitch but this glitch is not a one-color blob instead it has pattern on them, shown in the second image. The correct look of this view is shown in the third image. This pattern does not appear if long double is used, however on deeper zooms long double will not solve this.

However, the glitches CFJH encounters should be an ordinary one-color blob, so he has some other issue.


* glitch0.jpg (39.44 KB, 385x216 - viewed 267 times.)

* glitch1.jpg (40.57 KB, 385x216 - viewed 271 times.)

* glitch2.jpg (43.26 KB, 385x216 - viewed 276 times.)
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